docs: def friction_plate_Martin_VDI(Re, plate_enlargement_factor):
      r'''Calculates Darcy friction factor for single-phase flow in a 
      Chevron-style plate heat exchanger according to [1]_. 
      
      .. math::
          \frac{1}{\sqrt{f_d}} = \frac{\cos \phi}{\sqrt{0.28\tan\phi
          + 0.36\sin\phi + f_0/\cos(\phi)}} + \frac{1-\cos\phi}{\sqrt{3.8f_1}}
          
      .. math::
          f_0 = 64/Re \text{ for } Re < 2000
          
      .. math::
          f_0 = (1.56\ln Re - 3)^{-2} \text{ for } Re \ge 2000
          
      .. math::
          f_1 = \frac{597}{Re} + 3.85 \text{ for } Re < 2000
          
      .. math::
          f_1 = \frac{39}{Re^{0.289}} \text{ for } Re \ge 2000
          
      Parameters
      ----------
      Re : float
          Reynolds number with respect to the hydraulic diameter of the channels,
          [-]
      plate_enlargement_factor : float
          The extra surface area multiplier as compared to a flat plate
          caused the corrugations, [-]
  
      Returns
      -------
      fd : float
          Darcy friction factor [-]
  
      Notes
      -----
      Based on experimental data from Re from 200 - 10000 and enhancement 
      factors calculated with chevron angles of 0 to 80 degrees. See 
      `PlateExchanger` for further clarification on the definitions.
      
      The length the friction factor gets multiplied by is not the flow path
      length, but rather the straight path length from port to port as if there
      were no chevrons.
      
      Note there is a discontinuity at Re = 2000 for the transition from
      laminar to turbulent flow, although the literature suggests the transition
      is actually smooth.
      
      This is a revision of the Martin's earlier model, adjusted to predidct
      higher friction factors.
      
      There are three parameters in this model, a, b and c; it is posisble
      to adjust them to better fit a know exchanger's pressure drop.
      
      See Also
      --------
      friction_plate_Martin_1999
  
      Examples
      --------
      >>> friction_plate_Martin_VDI(Re=20000, plate_enlargement_factor=1.15)
      2.702534119024076
  
      References
      ----------
      .. [1] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition.
         Berlin; New York:: Springer, 2010.
      '''
      phi = plate_enlargement_factor
      
      if Re < 2000.:
          f0 = 64./Re
          f1 = 597./Re + 3.85
      else:
          f0 = (1.8*log10(Re) - 1.5)**-2
          f1 = 39.*Re**-0.289
          
      a, b, c = 3.8, 0.28, 0.36
          
      rhs = cos(phi)*(b*tan(phi) + c*sin(phi) + f0/cos(phi))**-0.5
      rhs += (1. - cos(phi))*(a*f1)**-0.5
      return rhs**-2.0